For the de-sitter patch our region of interest is area enclosed by the thermal opaque membrane on both sides in regions \(C\)  and \(R\) . When there is no island surface, then matter entanglement entropy appearing in the generalised entropy REF  will be given by the formula [1]}, [2]},
\(S_{\rm CEH}^{\mathcal {R}} = \frac{Q}{6} \log [d^2(b_2^+,b_2^-)],\) 
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